398 FINITE ELEMENT ANALYSIS orthotropic,no shear deformation,no restrained warping (Eq.6.8) N EA 0 0 0 就介 0 Elyy 0 0 (9.11) 0 0 0 0 [间 orthotropic,no shear deformation,restrained warping(Eqs.6.8 and 6.233) N EA 0 0 0 0 0 Elyy Ely: 0 0 0 Elyz El. 0 0 1101 (9.12) 0 0 0 0 熙 0 0 0 0 29 [可 orthotropic,shear deformation,restrained warping (Eqs.7.30,7.32,7.34,7.36) N EA 0 0 0 0 0 0 0 e 0 Elyy Elyz 0 0 0 0 0 dx: d 0 Elye El 0 0 0 0 0 dxy d 0 0 EL 0 0 0 0 doB dx 0 0 GI 0 0 0 29 0 0 0 0 Snt Yy 0 0 0 0 0 0 0 0 0 0 5 (E] (9.13) where [E]is the stiffness matrix for a beam element. 9.4 Sublaminate A laminate consisting of several plies may be analyzed by either plate(flat shell) or three-dimensional elements (Fig.9.2).For thick laminates neither of these Figure 9.2:Thick laminate (top),analysis with plate elements (left).analysis with three-dimensional elements(right).398 FINITE ELEMENT ANALYSIS orthotropic, no shear deformation, no restrained warping (Eq. 6.8)    N
M
y M
z T
   =      EA 0 00 0 EI yy EI yz 0 0 EI yz EI zz 0 00 0 GI t      % &' ( [E]    o x 1 ρy 1 ρz ϑ    (9.11) orthotropic, no shear deformation, restrained warping (Eqs. 6.8 and 6.233)    N
M
y M
z M
ω T
sv    =          EA 0 0 00 0 EI yy EI yz 0 0 0 EI yz EI zz 0 0 00 0 EI ω 0 00 00 GI t          % &' ( [E]    o x 1 ρy 1 ρz −dϑ dx ϑ    (9.12) orthotropic, shear deformation, restrained warping (Eqs. 7.30, 7.32, 7.34, 7.36)    N
M
y M
z M
ω T
sv V
y V
z T
ω    =                   EA 0 0 0 0000 0 EI yy EI yz 0 0000 0 EI yz EI zz 0 0000 00 0 EI ω 0000 00 00 GI t 000 00 0 00
Syy
Syz
Syω 00 0 00
Syz
Szz
Szω 00 0 00
Syω
Szω
Sωω                   % &' ( [E]    o x −dχz dx −dχy dx −dϑB dx ϑ γy γz ϑS    , (9.13) where [E] is the stiffness matrix for a beam element. 9.4 Sublaminate A laminate consisting of several plies may be analyzed by either plate (flat shell) or three-dimensional elements (Fig. 9.2). For thick laminates neither of these Figure 9.2: Thick laminate (top), analysis with plate elements (left), analysis with three-dimensional elements (right).